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Purpose: Nonstationarity of CT noise presents a major challenge to the assessment of image quality. This work presents
models for imaging performance in both filtered backprojection (FBP) and penalized likelihood (PL) reconstruction that
describe not only the dependence on the imaging chain but also the dependence on the object as well as the nonstationary
characteristics of the signal and noise. The work furthermore demonstrates the ability to impart control over the imaging
process by adjusting reconstruction parameters to exploit nonstationarity in a manner advantageous to a particular
imaging task.
Methods: A cascaded systems analysis model was used to model the local noise-power spectrum (NPS) and modulation
transfer function (MTF) for FBP reconstruction, with locality achieved by separate calculation of fluence and system
gain for each view as a function of detector location. The covariance and impulse response function for PL
reconstruction (quadratic penalty) were computed using the implicit function theorem and Taylor expansion.
Detectability index was calculated under the assumption of local stationarity to show the variation in task-dependent
image quality throughout the image for simple and complex, heterogeneous objects. Control of noise magnitude and
correlation was achieved by applying a spatially varying roughness penalty in PL reconstruction in a manner that
improved overall detectability.
Results: The models provide a foundation for task-based imaging performance assessment in FBP and PL image
reconstruction. For both FBP and PL, noise is anisotropic and varies in a manner dependent on the path length of each
view traversing the object. The anisotropy in turn affects task performance, where detectability is enhanced or
diminished depending on the frequency content of the task relative to that of the NPS. Spatial variation of the roughness
penalty can be exploited to control noise magnitude and correlation (and hence detectability).
Conclusions: Nonstationarity of image noise is a significant effect that can be modeled in both FBP and PL image
reconstruction. Prevalent spatial-frequency-dependent metrics of spatial resolution and noise can be analyzed under
assumptions of local stationarity, providing a means to analyze imaging performance as a function of location throughout
the image. Knowledgeable selection of a spatially-varying roughness penalty in PL can potentially improve local noise
and spatial resolution in a manner tuned to a particular imaging task.
Keywords: cascaded systems analysis, nonstationarity, filtered backprojection, penalized-likelihood reconstruction,
noise-power spectrum, covariance matrix, imaging task, detectability index
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